Electrical reactance
In electrical and electronic systems, reactance is the opposition of a circuit element to a change of or , due to that element's or . A built-up resists the change of voltage on the element, while a resists the change of current. The notion of reactance is similar to , but they differ in several respects. Capacitance and inductance are inherent properties of an element, just like resistance; their reactive effects are not exhibited under constant , but only when the conditions in the circuit change. Thus, the reactance differs with the rate of change, and is a constant only for circuits under of constant frequency. In of electric circuits, resistance is the real part of complex , while reactance is the imaginary part. Both share the same , the . An ideal has zero reactance, while ideal s and s consist entirely of reactance. Analysis In analysis, reactance is used to compute amplitude and phase changes of going through the circuit element. It is denoted by the symbol \scriptstyle{X} . Both reactance \scriptstyle{X} and \scriptstyle{R} are required to calculate the \scriptstyle{Z} . In some circuits one of these may dominate, but an approximate knowledge of the minor component is useful to determine if it may be neglected. : Z = R + jX\, :where * Z is the , measured in ohms. * R is the , measured in ohms. * X is the , measured in ohms. * j = \sqrt{-1} Both the \scriptstyle and the \scriptstyle{\theta} of the impedance depend on both the resistance and the reactance. : |Z| = \sqrt{ZZ^*} = \sqrt{R^2 + X^2} where Z^* is the of Z : \theta = \arctan{X \over R} The magnitude is the ratio of the and s, while the phase is the voltage–current phase difference. * If \scriptstyle{X > 0} , the reactance is said to be * If \scriptstyle{X = 0} , then the impedance is purely * If \scriptstyle{X < 0} , the reactance is said to be Capacitive reactance Capacitive reactance is an opposition to the change of voltage on a element. Capacitive reactance \scriptstyle{X_C} is to the signal \scriptstyle{f} (or ω) and the \scriptstyle{C} .Irwin, D. (2002). Basic Engineering Circuit Analysis, page 274. New York: John Wiley & Sons, Inc. : X_C = \frac {-1} {\omega C} = \frac {-1} {2\pi f C}\quad A capacitor consists of two s separated by an , also known as a . At low frequencies a capacitor is , as no flows in the dielectric. A voltage applied across a capacitor causes positive to accumulate on one side and negative to accumulate on the other side; the due to the accumulated charge is the source of the opposition to the current. When the associated with the charge exactly balances the applied voltage, the current goes to zero. Driven by an AC supply, a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge dissipates. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current. Inductive reactance Inductive reactance is an opposition to the change of current on a element. Inductive reactance \scriptstyle{X_L} is to the signal \scriptstyle{f} and the \scriptstyle{L} . : X_L = \omega L = 2\pi f L\quad An inductor consists of a . of electromagnetic induction gives the counter- \scriptstyle{\mathcal{E}} (voltage opposing current) due to a rate-of-change of \scriptstyle{B} through a current loop. : \mathcal{E} = - has a zero rate-of-change, and sees an inductor as a (it is typically made from a material with a low ). An has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency. Phase relationship The phase of the voltage across a purely reactive device (a device with a resistance of zero) lags the current by \scriptstyle{\pi/2} radians for a capacitive reactance and leads the current by \scriptstyle{\pi/2} radians for an inductive reactance. Note that without knowledge of both the resistance and reactance the relationship between voltage and current cannot be determined. The origin of the different signs for capacitive and inductive reactance is the phase factor in the impedance. : \tilde{Z}_C = {1 \over \omega C}e^{j(-{\pi \over 2})} = j\left({-1 \over \omega C}\right) = -jX_C\quad : \tilde{Z}_L = \omega Le^{j{\pi \over 2}} = j\omega L = jX_L\quad For a reactive component the sinusoidal voltage across the component is in quadrature (a \scriptstyle{\pi/2} phase difference) with the sinusoidal current through the component. The component alternately absorbs energy from the circuit and then returns energy to the circuit, thus a pure reactance does not dissipate power. See also * * * References # Pohl R. W. Elektrizitätslehre. – Berlin-Göttingen-Heidelberg: Springer-Verlag, 1960. # Popov V. P. The Principles of Theory of Circuits. – M.: Higher School, 1985, 496 p. (In Russian). # Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959. # | location = | isbn= 0-8053-9179-7}} External links * Interactive Java Tutorial on Inductive Reactance National High Magnetic Field Laboratory * Inductive Reactance: Endless Examples & Exercises Category:Physical quantities Category:Electronics terms Category:Physical quantities Category:Measurable quantities